Answers
Thus, It is possible to visually assess whether a limit exists as x approaches a by looking at the function f (x) and g (x) graphs, which are 1 and 5 when x is very close to x=a.
How would you define limit?In mathematics, a limit is the value that a function, a sequence, or an index approaches as an input or an index gets closer to a particular value. Limits are essential to the study of calculus and mathematical analysis since they are used to define continuity, derivatives, and integrals.
Here,
From the function f (x) and g graphs shown here ( x)
1) lim f (x) plus lim g ( x )
= -1 + 2 = 1
2) f (-1) + lim g ( x)
= 3 + 2
= 5
Therefore , the solution of the given problem of limit comes out be 5.
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Related Questions
The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)
Answers
The equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
Given that,
Three of a parallelogram's vertices have the coordinates (-3, 4), (-2, 1), and (2, 6).
We have to find what is the equation for the side of the line that contains the first two vertices' opposite side.
We know that,
The equation of the line is
y=mx+b
Here, we find m and d
Take the points (-3,4) (-2,1)
m = y₂-y₁ / x₂-x₁
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3
Now take point (2,6)
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b
We get m =-3 and b=12
The equation will be y=-3x+12
3x+y=12
Therefore, the equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
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Solve for x in the diagram below. ty
Answers
Answer:
x = 5
Step-by-step explanation:
90 - 50 = 40
40/8 = 5
Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)?
Answers
b.94 inches?
2. At a hardware store, a tool set normally costs $80. During a sale this week, the toc
set costs $12 less than usual. What percentage of the usual price is the savings?
Explain or show your reasoning.
Answers
Answer:
12%
Step-by-step explanation:
80-12=68
68/80= .85 so you’re paying 85% of the original which means you are saving 15%.
80*.15=12 which is the amount that was taken off
what does 2(3x+5) simplify to?
Answers
Answer:
6x+10
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
6x + 10
Step-by-step explanation:
2(3x + 5)
Distribute the 2.
When distributing, multiply the outside term(s) by the inside term(s).
2 * 3x = 6x
2 * 5 = 10
Combine them to get
6x + 10.
1.) Each row of the grocery store parking lot has 10 parking spots of equal width. What is the width for each spot?
2.) How many space is given for each parking spot at the mall parking lot if each spot has an equal width?
3.) Which location gives the greatest space for each parking lot?
(Ik this is a lot but can someone help me please I’m so confused)
Answers
When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.
what is equation ?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.
given
The grocery store is 31.92 wide overall, with 10 equally wide parking spaces.
If you assume that the width of these 10 parking spaces is equal to the width of the grocery store as a whole, you will have:
10x=31.92
on both sides of the equation, multiply by 10.
10x/10 = 31.92/10
x = 3.192
When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.
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The steepness of a ramp is graphed using the points (0,3) and (36,0). The steepness of a second ramp is represented by the function g(x)= -1/4x+2. What is the slope of the ramp?
Answers
The slope of a line is a measure of its steepness and can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the points (0,3) and (36,0) represent the coordinates of two points on the ramp. To find the slope of the ramp, we can plug these values into the formula:
slope = (0 - 3) / (36 - 0) = -3 / 36 = -1/12
The slope of the ramp is -1/12. This indicates that the ramp is relatively flat, as a negative slope means that the line is sloping downward.
To find the slope of the second ramp, represented by the function g(x) = -1/4x + 2, we can take the derivative of the function. The derivative of a function represents the slope of the function at any given point, and it is calculated using the formula:
derivative = f(x) = -1/4
The derivative of the function g(x) is a constant value of -1/4, which means that the slope of the second ramp is also -1/4. This is a steeper slope than the first ramp, as the value of the derivative is larger in magnitude.
Find the 7th term of the geometric sequence whose common ratio is 3/2 and whose first term is 5
Answers
The 7th term of the geometric sequence is 3675/64.
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio.
The 7th term of a geometric sequence can be found using the formula:
a_n = a_1 * (r)^(n-1) where a_1 is the first term of the sequence, r is the common ratio, and n is the position of the term in the sequence.
Given that the common ratio is 3/2 and the first term is 5, we can substitute these values into the formula:
a_7 = 5 * (3/2)^(7-1)
After solving the expression we get:
a_7 = 5 * (3/2)^6 = 5* (243/64) = 15*243/64 = 3675/64
So the 7th term of the geometric sequence is 3675/64.
Therefore, the 7th term of the geometric sequence is 3675/64.
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As long as the slope of the objectivefunction stays between the slopes of the binding constraints...
A: the optimal corner point wont change
B: the value of the objective function wont change
C: there will be alternative optimal solutions
D: there will be no slack in the solution
Answers
The correct answer is option A: the optimal corner point won't change.
The optimal corner point is the point where the objective function reaches its maximum value, with the constraints of the problem being satisfied. If the slope of the objective function stays between the slopes of the binding constraints, it means that the current optimal corner point will remain unchanged.
This is because if the objective function's slope is within the slopes of the binding constraints, then the set of points where the objective function reaches its maximum value will be the same. Therefore, the optimal corner point will not change.
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If radii of two concentric circle are 28 cm and 18 cm respectively if the perimeter and the area of the circle are numerically equal then find the radius of the circle
Answers
1. The area of two concentric circles with radii 28 cm and 18 cm is 460π cm^2.
2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle is 2 units.
What are concentric circles?
Concentric circles are those that share a common centre but have differing radii. It is described as two or more circles with the same centre, in other words.
The radii of two concentric circles are 28 cm and 18 cm.
The bigger circle has a radius of r1=28 cm and the smaller circle has the radius of r2=18 cm.
Area of two concentric circles is -
A = π[(r1)^2-(r2)^2]
A = π[(28)^2-(18)^2]
A = π[(28+18)(28-18)]
A = π[46 × 10]
A = 460π cm^2
Therefore, the area of concentric circle is 460π cm^2.
The formula for perimeter of the circle is 2πr, and the formula for the area of the circle is πr^2, where r is the radius of the circle.
Now, according to the data given the perimeter and area of the two circles are equal.
So, the equation will be 2πr = πr^2.
2πr = πr^2
2π = πr
r = 2 units
Therefore, the radius is 2 units.
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1. If radii of two concentric circle are 28 cm and 18 cm respectively. Find the area of the concentric circles.
2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle.
The mass of a dust particle is 6.54 x 10-7 kilograms. Which shows the mass
written as a decimal?
0.0000654 kg
0.00000654 kg
O 0.000000654 kg
0.0000000654 kg
Answers
Answer:
0.000000654 kg
Step-by-step explanation:
Is halting undecidable?
Answers
Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.
What is a tractable problem?a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.
Here,
There is no programme that can resolve the halting difficulty for sufficiently general computer programs,
making it the most frequently encountered problem that has been discovered to be insoluble.
The type of computer software we're discussing must be made clear.
Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.
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If triangle NPZ ~ triangle HBZ find the measure of angle B.
Please show the steps
Answers
The measure of angle B is 107°.
What do similar triangles mean?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given a triangle, NPZ is similar to triangle HBZ.
Which can also be written as ΔNPZ ≈ ΔHBZ
So, by equating the corresponding angles that are angle P = angle B:
8x-37°=180-(2x-5+42)°
10x=180
x=18°
So, H=36-5=31°
Since the sum of all angles in a triangle is 180°, angle B can be calculated as
B= 180°-(42+31)°
B=107°
Therefore the measure of angle B is 107 degrees
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On a coordinate plane, polygon S prime T prime U prime V prime has points (negative 2, 4), (negative 4, 1), (negative 2, negative 2), and (0, 1).
Given the dilation rule DO,1/3 (x, y) → (one-third x, one-third y)
and the image S'T'U'V', what are the coordinates of vertex V of the pre-image?
(0, 0)
(0, One-third)
(0, 1)
(0, 3)
Answers
The vertex of V' had a preimage of V(0, 3) as V' has a dilation of 3.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, On a coordinate plane, polygon S'T'U'V' has points (- 2, 4), (- 4, 1),
(- 2, - 2), and (0, 1) with a dilation rule DO,1/3 (x, y) to [(1/3)x, (1/3)y].
Therefore, The coordinates of the vertex V had a preimage of,
3(V'), which is 3(0, 1) = (0, 3).
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Please help!!!!! Look at picture, question 3. Links and silly answers will be reported. I’ll mark brainliest to whoever explains how they got their answer.Please please help!!
Answers
Answer:
72
Step-by-step explanation:
Ratio:2:3=2x:3x
2x+3x=180
5x=180
x=36
m ABD=36x2=72
how do i do this question
Answers
Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.
Step-by-step explanation:
Kourtney and Kayla are sisters who are taking the same classes this semester: MAT 003, CHM 131/3131A, and ACA 122. If kourtney earns a pee a P in MAT 003, a B in CHM 131A, and an A in ACA, then what will her GPA be?
A. 3. 5
B. 3. 2
C. 2. 58
D. 3. 8
Answers
the GPA for the current semester will be 3.5.
What is GPA?
A metric used to assess your performance throughout the course of your complete degree program is your grade point average.
The average grade point average (GPA) is a figure that represents your typical performance in classes over the course of a semester, term, or year. In line with how much you raise your overall grade point average over your time at the university, your typical GPA score will fluctuate (or, in some cases, how much you fall behind).
A pass grade is a P, an A is a grade of excellent performance worth 4 points per credit, and a B is a grade of good performance worth 3 points per credit. The grade averages do not take P grade into account.
MAT 003, CHM 131a, and ACA 122 each have three, one, and two credits. Thus, the final score is 3 + 1 + 1 = 5. P in MAT 003, B in CHM 131a, and A in ACA 122 are the grades she receives.
GPA can be calculated by
GPA = ( 3 × 1 + 4 × 1)/ 5
GPA = ( 3 + 4)/ 5
GPA = 3.5
Hence the GPA for the current semester will be 3.5.
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which decimal is equivalent to 25/6 ?
Answers
Answer:
4.1667
Your welcome!
Blake uses 2 gallons of gas to drive 34.6 miles in his car. Find the rate of change.
Answers
Answer:
17.3 miles / gallon
Step-by-step explanation:
RatesRates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)
SolutionGiven information from the question,
2 gallons = 34.6 miles
1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon
Write an equation for the nth term of the geometric sequences. Then Find a6
A. 2, 8, 32, 128,.
B. 0. 6, -3, 15, -75,.
C. -1/8, -1/4, -1/2, -1,.
D. 0. 1, 0. 9, 8. 1, 72. 9,
Answers
We want to find an equation and the sixth term of the given geometric sequence.
The equation is: [tex]a_{n} = 4*a_{n}-1[/tex] and the sixth term is equal to 512
What is Geometric sequence?In a geometric sequence, each term is a constant times the previous term, so the general relation is:
[tex]a_{n} = k*a_{n}-1[/tex]
Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:
[tex]8 = k*2\\8/2 = 4 = k[/tex]
Now we know the value of the constant, then the general formula is: [tex]a_{n} = 4*a_{n}-1[/tex]
Now we can use this to get the sixth term:
[tex]a_{6} = 4*a_{5}-1=4*128 = 512[/tex]
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As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 140 square yards in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places
Answers
The sprinkler should be set to rotate through the angle 6.42 degrees.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
r = 50 yards
Area, A = 140 square yards
Θ = angle
A= (Θ /360) πr²
140 = (Θ /360) * 3.14 * 50*50
Θ = (140*360)/(3.14*25*100) = 6.42 degrees
The sprinkler should be set to rotate through the angle 6.42 degrees.
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what is 5 divided by 1/4
Answers
Hope this helps!! May I have brainliest?
1/4 can be rewritten as a decimal, which would be .25.
How many times does .25 go into 5?
5/.25 = 20.
Or if you don’t want to convert the fraction into a decimal you could multiple by the reciprocal of 1/4:
5 / (1/4) = 5 * 4 = 20.
Either way 5 divided by 1/4 is 20.
PLZZZZ HELP!!!!!!!!!!!!!!!!!
Answers
Answer:
A=16.3 ft²
Step-by-step explanation:
we are given a composite figure, composing of a triangle and a semicircle
first, let's find the area of the triangle
we are given the height (5 ft) and the base of the triangle (4 ft)
the formula for the area of the triangle is given as bh/2, where b is the base and h is the height
substitute the known values into the formula
[tex]A_{triangle}[/tex]=bh/2
[tex]A_{triangle}[/tex]=(5*4)/2
[tex]A_{triangle}[/tex]=20/2=10 ft²
so the area of the triangle is 10 ft²
now to find the area of the semicircle:
the area of a semicircle is half the area of a circle; the area of a circle is given as πr², where r is the radius. Therefore, the area of a semicircle is (πr²)/2
4 ft isn't just the base of the triangle; it's also the diameter of the semicircle
however, we need the radius
the radius is half the diameter value
r=d/2
r=4/2
r=2 ft
so the radius is 4 feet
now find the area of the semicircle. Don't substitute for π just yet.
[tex]A_{semicircle}[/tex]=(πr²)/2
[tex]A_{semicircle}[/tex]=(π*2²)/2
[tex]A_{semicircle}[/tex]=4π/2
[tex]A_{semicircle}[/tex]=2π
π is often substituted as 3.14 or 22/7
so if we used 3.14 for instance:
[tex]A_{semicircle}[/tex]=6.28; rounded to the nearest tenth, that's 6.3 ft²
now add the two areas together to get the area of the composite figure
[tex]A_{compositefigure}[/tex]=[tex]A_{triangle}[/tex]+[tex]A_{semicircle}[/tex]
[tex]A_{compositefigure}[/tex]=10+6.3=16.3 ft²
Hope this helps! Good luck on your assignment!!
. In the cafeteria
3 out of every 5
students prefer
pizza. If there are
200 students in the
cafeteria how many
students prefer
pizza?
Answers
Answer:
120
Step-by-step explanation:
3/5 of 200 = 120
Step-by-step explanation: Write 3 out of every 5 students as a fraction, (3 over 5). Now divide 5 into 200. You get 40. Multiply that by 3, you get 120. (As a fraction it is 120 over 200). Therefore, 120 students prefer pizza.
Marcus bought a rug for a hallway. The rug measures 0.5 meter by 2.5 meters. Which is the area of the rug?
Answers
Answer:
1.25 meters
HOPE THIS HELPS
-Todo ❤️
Step-by-step explanation:
.5*2.5=1.25
what is x if 2/9+x=11/18?
Answers
Answer:
x = 7/18
Step-by-step explanation:
what is x if 2/9+x=11/18?
2/9 + x = 11/18
x = 11/18 - 2/9
x = 63/162
x = 7/18
check
2/9 + 7/18 = 11/18
11/18 = 11/18
the answer is goodI dont remember how to rewrite formulas properly
Answers
Answer:
h= (V/πr²)(3)
Step-by-step explanation:
Please help meeh thank u thank u
Answers
Answer:
The location would be between 4 and 5.
Step-by-step explanation:
The square root of 19 would be around 4.3. So you would put a mark between the two lines that are in between the 4 and 5.
A contractor is building a desk around a 15 x 20 rectangular swimming pool. He is going to build a 2-foot desk around the pool.
Answers
Answer:
[tex](15 + 2x)(20 + 2x)[/tex]
Step-by-step explanation:
Given
[tex]Length= 15[/tex]
[tex]Width = 20[/tex]
[tex]Deck = x[/tex] --- on both sides
Required
An expression for total area of the pool
Because the deck will be on both sides,
the dimension of the pool will be:
[tex]L = Length + 2 * deck[/tex] --- Length
[tex]L = 15 + 2x[/tex]
[tex]W = Width + 2 * deck[/tex] --- Width
[tex]W = 20 + 2x[/tex]
The total area of the pool is calculated as:
[tex]Area = Length * Width[/tex]
[tex]A = (15 + 2x) * (20 + 2x)[/tex]
[tex]A =(15 + 2x)(20 + 2x)[/tex]
Hence, the expression is: [tex](15 + 2x)(20 + 2x)[/tex]
What is the length of bc in the right triangle below
Answers
Answer:
C 82
Step-by-step explanation:
18^(2)+80^(2)=c^(2)